It's also possable that Eric is so humilated by the video being played in front of his family, bosses, strangers, parents of prospective students and that he is kicked out of the priesthood. All he wants to do is leave. He might think that he's still suffering from PTSD, that he went crazy, slept with Kristen, than tried to supress the memories because of guilt.

No drugs were found in his system, he himself doesn't know what happened so there's no way for him to prove, even to himself, that he wasn't breaking his vows by sleeping with Kristen willingly.

Nicole could be arguing that she believes him when he says that he doesn't know what happend. That he needs to stay and fight, to investigate until he uncovers the truth. But Eric gets angry because he is afraid that he is actually guilty.